# is-integer-like﻿, is-signed-integer-like

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template< class T > constexpr bool /*is-integer-like*/ = /* see description */; | (1) | (since C++20) (exposition only*)
template< class T > constexpr bool /*is-signed-integer-like*/ = /* see description */; | (2) | (since C++20) (exposition only*)

1) /*is-integer-like*/<T> is true if and only if `T` is an integer-like type.
2) /*is-signed-integer-like*/<T> is true if and only if `T` is a signed-integer-like type.

### Integer-class type

A type `T` is an integer-class type if it is in a set of implementation-defined types that behave as integer types do, as defined below. An integer-class type is not necessarily a class type.

An integer-class type can represent \(\scriptsize 2^N \)2N
consecutive integers, where N, a positive integer, is called the width of the integer-class type.

An integer-class type is either signed or unsigned:

- A signed integer class type can represent all integers in `[`\(\scriptsize -2^{N-1} \)-2N-1
  `,` \(\scriptsize 2^{N-1}-1 \)2N-1
  -1`]`, where N is greater than the width of every signed integral type.
- An unsigned integer class type can represent all integers in `[`\(\scriptsize 0 \)0`,` \(\scriptsize 2^N-1 \)2N
  -1`]`, where N is greater than the width of every unsigned integral type.

All integer-class types model `regular` and `three_way_comparable`<std::strong_ordering>.

A value-initialized object of integer-class type has value â0â.

An expression E of integer-class type `T` is contextually convertible to bool as if by bool(E != T(0)).

### Integer-like type

A type other than (possibly cv-qualified) bool is integer-like if it models `integral` or if it is an integer-class type.

- An integer-like type is signed-integer-like if it models `signed_integral` or if it is a signed-integer-class type.
- An integer-like type is unsigned-integer-like if it models `unsigned_integral` or if it is an unsigned-integer-class type.

### Required behaviors

Expressions of integer-class type are explicitly convertible to any integer-like type, and implicitly convertible to any integer-class type of equal or greater width and the same signedness. Expressions of integral type are both implicitly and explicitly convertible to any integer-class type. Conversions between integral and integer-class types and between two integer-class types do not exit via an exception. The result of such a conversion is the unique value of the destination type that is congruent to the source modulo \(\scriptsize 2^N \)2N
, where N is the width of the destination type.

Let `Int<T>` denote the following type:

- If `T` is an integer-class type, `Int<T>` is a unique hypothetical extended integer type of the same signedness with the same width as `T`.
- If `T` is an integral type, let `Int<T>` is the same type as `T`.

Given the following types, values and operators:

Type | Definition
`IC` | an integer-class type
`IL` | an integer-like type
Value | Definition
a | an object of type `IC`
b | an object of type `IL`
c | an lvalue of an integeral type
x | an object of type `Int<IC>` that represent the same value as a
y | an object of type `Int<IL>` that represent the same value as b
Operator | Definition
@= | one of +=, -=, *=, /=, %=, &=, |=, ^=, <<= and >>=
@ | one of +, -, *, /, %, &, |, ^, <<, >>, &&, ||, ==, !=, <, >, <=, >=, <=> and ,

The following expressions must be well-formed and have their specified result and effects if the specified conditions are satisfied:

Expression | Condition | Result | Effects
--- | --- | --- | ---
a++ | No condition | a prvalue of type `IC` whose value is equal to that of a prior to the evaluation | modifies the value of a by adding 1 to it
a-- | modifies the value of a by subtracting 1 to it
++a | expression-equivalent to a += 1
--a | expression-equivalent to a -= 1
&a | expression-equivalent to std::addressof(a)
!a | !x is well-formed | same as !x
+a | +x is well-formed | same as +x, but has type `IC` | same as +x
-a | -x is well-formed | same as -x, but has type `IC` | same as -x
~a | ~x is well-formed | same as ~x, but has type `IC` | same as ~x
c @= a | c @= x is well-formed | an lvalue referring to c | same as c @= x
a @= b | x @= y is well-formed | an lvalue referring to a | same as x @= y, except that the value that would be stored into x is stored into a
a @ b | x @ y is well-formed | same as x @ y, but the result type is different: If x @ y is of type `Int<IC>`, the result has type `IC`. If x @ y is of type `Int<IL>`, the result has type `IL`. If x @ y is of any other type `T`, the result has type `T`. | same as x @ y
b @ a | y @ x is well-formed | same as y @ x, but the result type is different: If y @ x is of type `Int<IC>`, the result has type `IC`. If y @ x is of type `Int<IL>`, the result has type `IL`. If y @ x is of any other type `T`, the result has type `T`. | same as y @ x

### Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR | Applied to | Behavior as published | Correct behavior
--- | --- | --- | ---
LWG 3366 (P2393R1) | C++20 | the conversion between an integer-class type and its corresponding integer type was not guaranteed to produce a representable value | guaranteed
LWG 3376 (P2393R1) | C++20 | integer-class types could only be class types | also allowed non-class types
LWG 3467 | C++20 | bool was considered as an integer-like type | excluded
LWG 3575 (P2393R1) | C++20 | integer-class types were not guaranteed to be three-way-comparable | guaranteed

### See also

weakly_incrementable (C++20) | specifies that a `semiregular` type can be incremented with pre- and post-increment operators (concept)

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